On some new properties of the spherical curvature of stereographically projected analytic curves

Stephen M. Zemyan

International Journal of Mathematics and Mathematical Sciences, 2003, vol. 2003, 1-12

Abstract:

We discover new information about the spherical curvature of stereographically projected analytic curves. To do so, we first state formulas for the spherical curvature and spherical torsion of the curves on S 2 which result after stereographically projecting the image curves of analytic, univalent functions belonging to the class 𝒮 . We then derive results concerning the location of the critical points of the spherical curvature, considered both as a function of one and two variables. Further analysis leads to a maximum principle for the spherical curvature functions.

Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:721818

DOI: 10.1155/S016117120320819X

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